


Counting Backwards from Infinity

by themazeballet



Category: Sherlock (TV)
Genre: Gen
Language: English
Status: Completed
Published: 2011-04-11
Updated: 2011-04-11
Packaged: 2017-10-17 22:41:37
Rating: Teen And Up Audiences
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 1
Words: 1,092
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/182063
Author URL: https://archiveofourown.org/users/themazeballet/pseuds/themazeballet





	Counting Backwards from Infinity

**Author's Note:**

  * For [MadXStitcher](https://archiveofourown.org/users/MadXStitcher/gifts).



They had been easy patterns at first. Even numbers starting at two, multiples of nine, prime numbers except one.

But then the cases got harder. Fibonacci's number, the square root of all prime numbers except for one, pi to the hundredth digit, 16!. His collection of books went from forensics to Natural Mathematics. His moleskine notebook held more fractals than notes on cases.

He learned math in binary, covering his bedroom in long sequences of zeroes and ones--and then, pi to the three hundredth digit.

John didn't say anything, and mourned the deposit they would never get back privately.

Anything, anything, to stop the noise crowding his mind. The four million Londoners with their four million voices with their four million problems, all listening to different music and smelling differently and lips moving and no sound coming out...

So he counted. In a crime scene, cleared of everything except the low talking and the smells, he counted. And when he counted, everything came out. Anything that didn't fit the pattern of his low, toneless counting jumped out as if it were highlighted in neon lighting.

Sometimes, he'd have to be reminded. That's where Lestrade's notebook came in. So many glorious patterns to count off. So many numbers to run through. Sherlock thought he really ought to thank Lestrade's sister, but then he realised that he wasn't one for sending thank you notes.

"I know pi to three hundred and twenty-five digits," he said one day, standing over a victim's bed, staring at the ligature marks around her neck.

"Pi is a non-repeating decimal," John said from the door (his new after-shave was too strong, Sherlock had told him). "There's no pattern in pi."

"I've made one. In a manner of speaking. It's how I came to memorise the first three hundred and twenty-five digits. I've grouped them." He looked at the woman lying in bed. "The ligature marks are old. She practised self-asphyxiation."

John watched Sherlock as he knelt next to the woman. He could hear Sherlock murmuring.

+++

Sherlock had no problems sleeping whilst on a case. It was the long days when nothing caught his eye that he stayed up, playing his violin (music was nothing but a pattern of notes, easy) and counting. Sometimes John stayed up to listen to him count, sometimes he stormed down to tell Sherlock exactly what he thought of his patterns.

When yelling didn't work, or pleading his case, or out and out threatening, John would make a cup of tea and sit down in front of Sherlock.

"What's your pattern for pi?"

"Prime numbers. Except for one."

"Why not one?"

"It's only divisible by itself. It's not quite prime but it can't be described in any other fashion. Dividing by one is its own rule." Sherlock plucked at the strings of his violin idly. "One is, for lack of a better word, odd."

"One is the loneliest number," John sang tonelessly. Sherlock frowned at him. "Never mind. I do wish you'd stop playing your violin at three in the morning."

"I'm bored."

"And I'm tired."

"I could play you a lullaby."

John sighed. "I don't have a choice in the matter, do I?"

"Not particularly," Sherlock replied.

John sighed again. "Play on then, maestro, play on."

+++

There was a number written above this body. Sherlock stared at it. **226**. Sherlock frowned.

"What does it mean, do you think?" Lestrade asked as Sherlock got to his observation of the body.

"He's missing a ring," Sherlock said, opening the bedside table drawers to make sure the victim hadn't just taken it off before going to bed. "The sum of those digits is ten. Or one." He frowned again. "He's the first." He stood up, brushing his coat. "This case is for me..."

Lestrade rubbed his jaw. "The last time a case was for you, we had explosions across the city."

"I can't say that won't happen again."

Lestrade licked his lips. "Well." He turned out of the room, pulling his mobile out of his pocket. Sherlock looked back at the body, gazing at the man's face. His eyes were still open.

+++

The next body had the number **374** painted above it. "Two," Sherlock said.

"And how many until you figure it out?" Lestrade asked.

"I suppose when I find the pattern," Sherlock replied, picking up the woman's hand. "She's missing a ring as well. There are hundreds, thousands of three digit numbers that equal out to three." He shrugged. "Two numbers don't make a pattern."

"So...you're saying at least one more person has to die before you can figure out a pattern?" John asked.

"Look! The difference between these two numbers is 152, they're both even, the least common multiple is..." Sherlock stared at the victim. "The least common multiple is... _one_."

"Bloody helpful, that," John muttered. "So, we're looking for a maths teacher, is that it?"

Sherlock shrugged. "It wouldn't be the first time."

+++

The third body had the number **426** painted above it, and Sherlock almost leapt for joy. "Prime factors! How ingeniously simple! They all have two as a prime factor. They're missing their wedding rings, all of them." Sherlock reached down and closed the victim's eyes. "We're looking for a marriage counsellor who was also..." He smirked at John "...A maths professor."

"It only took you three victims this time," Lestrade said. "Mind you don't repeat that again."

"I will endeavour never to catch the interest of a former maths professor who is currently a marriage counsellor," Sherlock replied. "It's not in my usual habit to do so, that is correct."

Lestrade rolled his eyes. "I meant letting more people die so you can figure out your little patterns." He gestured for one of the CSI people. "Look for a diary, some sort of date book. We're looking for a standing appointment with a counsellor or a therapist."

Sherlock stared at the number above the victim's head. "The next number would have been 544," he said, and turned away, walking out of the room. "544, 626, 762..."

"It's a bit not good to go off counting off more victims."

"Well, we do have to find the woman before she decides to kill again."

"It's a woman?"

"No struggle. Which doesn't mean much, but all the victims knew their attacker and trusted her. Also, they were all poisoned." He looked back. "Poison is quite popular with women, has been historically."

"Sometimes I wonder what goes on in that head of yours."

"Much more than goes on in yours, I assure you."


End file.
